TSTP Solution File: SYN181-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN181-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:54:05 EDT 2022
% Result : Unsatisfiable 1.10s 0.95s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN181-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 02:03:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.10/0.95 % SZS status Unsatisfiable
% 1.10/0.95 % SZS output start Proof
% 1.10/0.95 tff(q2_type, type, (
% 1.10/0.95 q2: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(d_type, type, (
% 1.10/0.95 d: $i)).
% 1.10/0.95 tff(b_type, type, (
% 1.10/0.95 b: $i)).
% 1.10/0.95 tff(m0_type, type, (
% 1.10/0.95 m0: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(q1_type, type, (
% 1.10/0.95 q1: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(c_type, type, (
% 1.10/0.95 c: $i)).
% 1.10/0.95 tff(n0_type, type, (
% 1.10/0.95 n0: ( $i * $i ) > $o)).
% 1.10/0.95 tff(p0_type, type, (
% 1.10/0.95 p0: ( $i * $i ) > $o)).
% 1.10/0.95 tff(r1_type, type, (
% 1.10/0.95 r1: $i > $o)).
% 1.10/0.95 tff(q0_type, type, (
% 1.10/0.95 q0: ( $i * $i ) > $o)).
% 1.10/0.95 tff(s0_type, type, (
% 1.10/0.95 s0: $i > $o)).
% 1.10/0.95 tff(k0_type, type, (
% 1.10/0.95 k0: $i > $o)).
% 1.10/0.95 tff(m3_type, type, (
% 1.10/0.95 m3: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(p2_type, type, (
% 1.10/0.95 p2: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(n1_type, type, (
% 1.10/0.95 n1: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(q4_type, type, (
% 1.10/0.95 q4: ( $i * $i ) > $o)).
% 1.10/0.95 tff(k3_type, type, (
% 1.10/0.95 k3: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(m1_type, type, (
% 1.10/0.95 m1: ( $i * $i * $i ) > $o)).
% 1.10/0.95 tff(e_type, type, (
% 1.10/0.95 e: $i)).
% 1.10/0.95 tff(1,assumption,(~m0(b, d, d)), introduced(assumption)).
% 1.10/0.95 tff(2,plain,
% 1.10/0.95 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(3,plain,
% 1.10/0.95 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.10/0.95 inference(quant_intro,[status(thm)],[2])).
% 1.10/0.95 tff(4,plain,
% 1.10/0.95 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.10/0.95 tff(6,plain,
% 1.10/0.95 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.10/0.95 tff(7,plain,(
% 1.10/0.95 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.10/0.95 inference(skolemize,[status(sab)],[6])).
% 1.10/0.95 tff(8,plain,
% 1.10/0.95 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.10/0.95 tff(9,plain,
% 1.10/0.95 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, d)),
% 1.10/0.95 inference(quant_inst,[status(thm)],[])).
% 1.10/0.95 tff(10,plain,
% 1.10/0.95 ($false),
% 1.10/0.95 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.10/0.95 tff(11,plain,(m0(b, d, d)), inference(lemma,lemma(discharge,[]))).
% 1.10/0.95 tff(12,plain,
% 1.10/0.95 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(13,plain,
% 1.10/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[12])).
% 1.10/0.95 tff(14,plain,
% 1.10/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(15,plain,
% 1.10/0.95 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(16,plain,
% 1.10/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[15])).
% 1.10/0.95 tff(17,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 1.10/0.95 tff(18,plain,
% 1.10/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.10/0.95 tff(19,plain,
% 1.10/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.10/0.95 tff(20,plain,(
% 1.10/0.95 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(skolemize,[status(sab)],[19])).
% 1.10/0.95 tff(21,plain,
% 1.10/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.10/0.95 tff(22,plain,
% 1.10/0.95 (n0(d, c) <=> n0(d, c)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(23,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 1.10/0.95 tff(24,plain,
% 1.10/0.95 (n0(d, c)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.10/0.95 tff(25,plain,
% 1.10/0.95 (p0(c, b) <=> p0(c, b)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(26,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.10/0.95 tff(27,plain,
% 1.10/0.95 (p0(c, b)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.10/0.95 tff(28,plain,
% 1.10/0.95 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(29,plain,
% 1.10/0.95 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 1.10/0.95 inference(quant_inst,[status(thm)],[])).
% 1.10/0.95 tff(30,plain,
% 1.10/0.95 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.10/0.95 tff(31,plain,
% 1.10/0.95 (q1(b, c, b)),
% 1.10/0.95 inference(unit_resolution,[status(thm)],[30, 27, 24, 21])).
% 1.10/0.95 tff(32,plain,
% 1.10/0.95 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(33,plain,
% 1.10/0.95 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[32])).
% 1.10/0.95 tff(34,plain,
% 1.10/0.95 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(35,plain,
% 1.10/0.95 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(36,plain,
% 1.10/0.95 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[35])).
% 1.10/0.95 tff(37,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 1.10/0.95 tff(38,plain,
% 1.10/0.95 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.10/0.95 tff(39,plain,
% 1.10/0.95 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.10/0.95 tff(40,plain,(
% 1.10/0.95 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(skolemize,[status(sab)],[39])).
% 1.10/0.95 tff(41,plain,
% 1.10/0.95 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.10/0.95 tff(42,plain,
% 1.10/0.95 (((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))) <=> ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(43,plain,
% 1.10/0.95 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 1.10/0.95 inference(quant_inst,[status(thm)],[])).
% 1.10/0.95 tff(44,plain,
% 1.10/0.95 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.10/0.95 tff(45,plain,
% 1.10/0.95 (q2(b, b, b)),
% 1.10/0.95 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 1.10/0.95 tff(46,plain,
% 1.10/0.95 (p0(b, d) <=> p0(b, d)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(47,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 1.10/0.95 tff(48,plain,
% 1.10/0.95 (p0(b, d)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.10/0.95 tff(49,plain,
% 1.10/0.95 (n0(d, b) <=> n0(d, b)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(50,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 1.10/0.95 tff(51,plain,
% 1.10/0.95 (n0(d, b)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.10/0.95 tff(52,plain,
% 1.10/0.95 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(53,plain,
% 1.10/0.96 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(54,plain,
% 1.10/0.96 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.10/0.96 tff(55,plain,
% 1.10/0.96 (q1(d, b, d)),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[54, 51, 48, 21])).
% 1.10/0.96 tff(56,plain,
% 1.10/0.96 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(57,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[56])).
% 1.10/0.96 tff(58,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(59,plain,
% 1.10/0.96 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(60,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[59])).
% 1.10/0.96 tff(61,plain,
% 1.10/0.96 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(62,plain,
% 1.10/0.96 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[61])).
% 1.10/0.96 tff(63,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 1.10/0.96 tff(64,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.10/0.96 tff(65,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.10/0.96 tff(66,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[65, 58])).
% 1.10/0.96 tff(67,plain,(
% 1.10/0.96 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(skolemize,[status(sab)],[66])).
% 1.10/0.96 tff(68,plain,
% 1.10/0.96 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[67, 57])).
% 1.10/0.96 tff(69,plain,
% 1.10/0.96 (q0(b, b) <=> q0(b, b)),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(70,axiom,(q0(b, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_6')).
% 1.10/0.96 tff(71,plain,
% 1.10/0.96 (q0(b, b)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.10/0.96 tff(72,plain,
% 1.10/0.96 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | r1(b) | (~q1(d, b, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(73,plain,
% 1.10/0.96 (((~q0(b, b)) | (~q1(d, b, d)) | r1(b)) <=> ((~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(74,plain,
% 1.10/0.96 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | r1(b) | (~q1(d, b, d))))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[73])).
% 1.10/0.96 tff(75,plain,
% 1.10/0.96 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.10/0.96 inference(transitivity,[status(thm)],[74, 72])).
% 1.10/0.96 tff(76,plain,
% 1.10/0.96 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(77,plain,
% 1.10/0.96 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.10/0.96 tff(78,plain,
% 1.10/0.96 (r1(b)),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[77, 71, 68, 55])).
% 1.10/0.96 tff(79,plain,
% 1.10/0.96 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(80,plain,
% 1.10/0.96 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[79])).
% 1.10/0.96 tff(81,plain,
% 1.10/0.96 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(82,plain,
% 1.10/0.96 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((q2(C, D, C) | (~r1(D))) <=> ((~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> (((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))))), rewrite((((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> (((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))))), rewrite((((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> (((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))))), rewrite((((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(83,plain,
% 1.10/0.96 (![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[82])).
% 1.10/0.96 tff(84,axiom,(![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 1.10/0.96 tff(85,plain,
% 1.10/0.96 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.10/0.96 tff(86,plain,
% 1.10/0.96 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.10/0.96 tff(87,plain,(
% 1.10/0.96 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(skolemize,[status(sab)],[86])).
% 1.10/0.96 tff(88,plain,
% 1.10/0.96 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[87, 80])).
% 1.10/0.96 tff(89,plain,
% 1.10/0.96 (k0(b) <=> k0(b)),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(90,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.10/0.96 tff(91,plain,
% 1.10/0.96 (k0(b)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.10/0.96 tff(92,plain,
% 1.10/0.96 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(93,plain,
% 1.10/0.96 (((~m0(b, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d)) <=> ((~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(94,plain,
% 1.10/0.96 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(b, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d)))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[93])).
% 1.10/0.96 tff(95,plain,
% 1.10/0.96 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(b, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))),
% 1.10/0.96 inference(transitivity,[status(thm)],[94, 92])).
% 1.10/0.96 tff(96,plain,
% 1.10/0.96 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(b, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(97,plain,
% 1.10/0.96 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.10/0.96 tff(98,plain,
% 1.10/0.96 (q2(d, b, d)),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[97, 91, 88, 78, 45, 11])).
% 1.10/0.96 tff(99,plain,
% 1.10/0.96 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(100,plain,
% 1.10/0.96 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[99])).
% 1.10/0.96 tff(101,plain,
% 1.10/0.96 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(102,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 1.10/0.96 tff(103,plain,
% 1.10/0.96 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.10/0.96 tff(104,plain,(
% 1.10/0.96 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.10/0.96 inference(skolemize,[status(sab)],[103])).
% 1.10/0.96 tff(105,plain,
% 1.10/0.96 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[104, 100])).
% 1.10/0.96 tff(106,plain,
% 1.10/0.96 (^[B: $i] : refl((p2(B, B, B) | (~n1(d, d, B))) <=> (p2(B, B, B) | (~n1(d, d, B))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(107,plain,
% 1.10/0.96 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[106])).
% 1.10/0.96 tff(108,plain,
% 1.10/0.96 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(109,axiom,(![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_153')).
% 1.10/0.96 tff(110,plain,
% 1.10/0.96 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.10/0.96 tff(111,plain,(
% 1.10/0.96 ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 1.10/0.96 inference(skolemize,[status(sab)],[110])).
% 1.10/0.96 tff(112,plain,
% 1.10/0.96 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.10/0.96 tff(113,plain,
% 1.10/0.96 (n1(d, d, d) <=> n1(d, d, d)),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(114,plain,
% 1.10/0.96 ((n1(d, d, d) | $false) <=> n1(d, d, d)),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(115,plain,
% 1.10/0.96 ((~$true) <=> $false),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(116,axiom,(q0(d, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 1.10/0.96 tff(117,plain,
% 1.10/0.96 (q0(d, d) <=> $true),
% 1.10/0.96 inference(iff_true,[status(thm)],[116])).
% 1.10/0.96 tff(118,plain,
% 1.10/0.96 ((~q0(d, d)) <=> (~$true)),
% 1.10/0.96 inference(monotonicity,[status(thm)],[117])).
% 1.10/0.96 tff(119,plain,
% 1.10/0.96 ((~q0(d, d)) <=> $false),
% 1.10/0.96 inference(transitivity,[status(thm)],[118, 115])).
% 1.10/0.96 tff(120,plain,
% 1.10/0.96 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | $false)),
% 1.10/0.96 inference(monotonicity,[status(thm)],[119])).
% 1.10/0.96 tff(121,plain,
% 1.10/0.96 ((n1(d, d, d) | (~q0(d, d))) <=> n1(d, d, d)),
% 1.10/0.96 inference(transitivity,[status(thm)],[120, 114])).
% 1.10/0.96 tff(122,plain,
% 1.10/0.96 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(123,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 1.10/0.96 tff(124,plain,
% 1.10/0.96 (n1(d, d, d) | (~q0(d, d))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.10/0.96 tff(125,plain,
% 1.10/0.96 (n1(d, d, d) | (~q0(d, d))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[124, 122])).
% 1.10/0.96 tff(126,plain,
% 1.10/0.96 (n1(d, d, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[125, 121])).
% 1.10/0.96 tff(127,plain,
% 1.10/0.96 (n1(d, d, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[126, 113])).
% 1.10/0.96 tff(128,plain,
% 1.10/0.96 (((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))) <=> ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(129,plain,
% 1.10/0.96 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(130,plain,
% 1.10/0.96 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.10/0.96 tff(131,plain,
% 1.10/0.96 (p2(d, d, d)),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[130, 127, 112])).
% 1.10/0.96 tff(132,plain,
% 1.10/0.96 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(d, d, d)) | m3(d, d, d))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(d, d, d)) | m3(d, d, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(133,plain,
% 1.10/0.96 ((m3(d, d, d) | (~p2(d, d, d))) <=> ((~p2(d, d, d)) | m3(d, d, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(134,plain,
% 1.10/0.96 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(d, d, d) | (~p2(d, d, d)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(d, d, d)) | m3(d, d, d)))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[133])).
% 1.10/0.96 tff(135,plain,
% 1.10/0.96 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(d, d, d) | (~p2(d, d, d)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(d, d, d)) | m3(d, d, d))),
% 1.10/0.96 inference(transitivity,[status(thm)],[134, 132])).
% 1.10/0.96 tff(136,plain,
% 1.10/0.96 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(d, d, d) | (~p2(d, d, d)))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(137,plain,
% 1.10/0.96 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(d, d, d)) | m3(d, d, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.10/0.96 tff(138,plain,
% 1.10/0.96 (m3(d, d, d)),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[137, 131, 105])).
% 1.10/0.96 tff(139,plain,
% 1.10/0.96 ((~q4(d, b)) <=> (~q4(d, b))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(140,axiom,(~q4(d, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.10/0.96 tff(141,plain,
% 1.10/0.96 (~q4(d, b)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.10/0.96 tff(142,plain,
% 1.10/0.96 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(143,plain,
% 1.10/0.96 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[142])).
% 1.10/0.96 tff(144,plain,
% 1.10/0.96 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(145,plain,
% 1.10/0.96 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q4(B, C) | (~k3(D, D, B))) <=> ((~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> (((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))))), rewrite((((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> (((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))))), rewrite((((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(146,plain,
% 1.10/0.96 (![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[145])).
% 1.10/0.96 tff(147,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 1.10/0.96 tff(148,plain,
% 1.10/0.96 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.10/0.96 tff(149,plain,
% 1.10/0.96 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[148, 144])).
% 1.10/0.96 tff(150,plain,(
% 1.10/0.96 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(skolemize,[status(sab)],[149])).
% 1.10/0.96 tff(151,plain,
% 1.10/0.96 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[150, 143])).
% 1.10/0.96 tff(152,plain,
% 1.10/0.96 (^[D: $i, E: $i, C: $i] : refl((m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))) <=> (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(153,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))) <=> ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[152])).
% 1.10/0.96 tff(154,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))) <=> ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(155,plain,
% 1.10/0.96 (^[D: $i, E: $i, C: $i] : trans(monotonicity(rewrite((m1(C, C, C) | (~q0(D, E))) <=> (m1(C, C, C) | (~q0(D, E)))), (((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> ((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))))), rewrite(((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))), (((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(156,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : ((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[155])).
% 1.10/0.96 tff(157,axiom,(![D: $i, E: $i, C: $i] : ((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_018')).
% 1.10/0.96 tff(158,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.10/0.96 tff(159,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[158, 154])).
% 1.10/0.96 tff(160,plain,(
% 1.10/0.96 ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(skolemize,[status(sab)],[159])).
% 1.10/0.96 tff(161,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[160, 153])).
% 1.10/0.96 tff(162,plain,
% 1.10/0.96 (q0(e, d) <=> q0(e, d)),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(163,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 1.10/0.96 tff(164,plain,
% 1.10/0.96 (q0(e, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.10/0.96 tff(165,plain,
% 1.10/0.96 (((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | ((~q0(e, d)) | m1(d, d, d))) <=> ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (~q0(e, d)) | m1(d, d, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(166,plain,
% 1.10/0.96 ((m1(d, d, d) | (~q0(e, d)) | (~q0(e, d))) <=> ((~q0(e, d)) | m1(d, d, d))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(167,plain,
% 1.10/0.96 (((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (m1(d, d, d) | (~q0(e, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | ((~q0(e, d)) | m1(d, d, d)))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[166])).
% 1.10/0.96 tff(168,plain,
% 1.10/0.96 (((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (m1(d, d, d) | (~q0(e, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (~q0(e, d)) | m1(d, d, d))),
% 1.10/0.96 inference(transitivity,[status(thm)],[167, 165])).
% 1.10/0.96 tff(169,plain,
% 1.10/0.96 ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (m1(d, d, d) | (~q0(e, d)) | (~q0(e, d)))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(170,plain,
% 1.10/0.96 ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (~q0(e, d)) | m1(d, d, d)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.10/0.96 tff(171,plain,
% 1.10/0.96 (m1(d, d, d)),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[170, 164, 161])).
% 1.10/0.96 tff(172,plain,
% 1.10/0.96 (^[D: $i, E: $i, C: $i] : refl(((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)) <=> ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(173,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)) <=> ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[172])).
% 1.10/0.96 tff(174,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)) <=> ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(175,plain,
% 1.10/0.96 (^[D: $i, E: $i, C: $i] : trans(monotonicity(rewrite((k3(C, C, C) | (~p2(D, E, D))) <=> ((~p2(D, E, D)) | k3(C, C, C))), (((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E))) <=> (((~p2(D, E, D)) | k3(C, C, C)) | (~m1(C, C, E))))), rewrite((((~p2(D, E, D)) | k3(C, C, C)) | (~m1(C, C, E))) <=> ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))), (((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E))) <=> ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(176,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : ((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E))) <=> ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[175])).
% 1.10/0.96 tff(177,axiom,(![D: $i, E: $i, C: $i] : ((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_196')).
% 1.10/0.96 tff(178,plain,
% 1.10/0.96 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.10/0.96 tff(179,plain,
% 1.10/0.97 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.97 inference(modus_ponens,[status(thm)],[178, 174])).
% 1.10/0.97 tff(180,plain,(
% 1.10/0.97 ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.97 inference(skolemize,[status(sab)],[179])).
% 1.10/0.97 tff(181,plain,
% 1.10/0.97 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 1.10/0.97 inference(modus_ponens,[status(thm)],[180, 173])).
% 1.10/0.97 tff(182,plain,
% 1.10/0.97 (((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | ((~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d))) <=> ((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | (~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d))),
% 1.10/0.97 inference(rewrite,[status(thm)],[])).
% 1.10/0.97 tff(183,plain,
% 1.10/0.97 ((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | ((~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d))),
% 1.10/0.97 inference(quant_inst,[status(thm)],[])).
% 1.10/0.97 tff(184,plain,
% 1.10/0.97 ((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | (~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d)),
% 1.10/0.97 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.10/0.97 tff(185,plain,
% 1.10/0.97 (k3(d, d, d)),
% 1.10/0.97 inference(unit_resolution,[status(thm)],[184, 131, 181, 171])).
% 1.10/0.97 tff(186,plain,
% 1.10/0.97 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(d, b) | (~k3(d, d, d)) | (~m3(d, d, d)) | (~q2(d, b, d)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(d, b) | (~k3(d, d, d)) | (~m3(d, d, d)) | (~q2(d, b, d)))),
% 1.10/0.97 inference(rewrite,[status(thm)],[])).
% 1.10/0.97 tff(187,plain,
% 1.10/0.97 (((~m3(d, d, d)) | (~q2(d, b, d)) | (~k3(d, d, d)) | q4(d, b)) <=> (q4(d, b) | (~k3(d, d, d)) | (~m3(d, d, d)) | (~q2(d, b, d)))),
% 1.10/0.97 inference(rewrite,[status(thm)],[])).
% 1.10/0.97 tff(188,plain,
% 1.10/0.97 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(d, d, d)) | (~q2(d, b, d)) | (~k3(d, d, d)) | q4(d, b))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(d, b) | (~k3(d, d, d)) | (~m3(d, d, d)) | (~q2(d, b, d))))),
% 1.10/0.97 inference(monotonicity,[status(thm)],[187])).
% 1.10/0.97 tff(189,plain,
% 1.10/0.97 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(d, d, d)) | (~q2(d, b, d)) | (~k3(d, d, d)) | q4(d, b))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(d, b) | (~k3(d, d, d)) | (~m3(d, d, d)) | (~q2(d, b, d)))),
% 1.10/0.97 inference(transitivity,[status(thm)],[188, 186])).
% 1.10/0.97 tff(190,plain,
% 1.10/0.97 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(d, d, d)) | (~q2(d, b, d)) | (~k3(d, d, d)) | q4(d, b))),
% 1.10/0.97 inference(quant_inst,[status(thm)],[])).
% 1.10/0.97 tff(191,plain,
% 1.10/0.97 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(d, b) | (~k3(d, d, d)) | (~m3(d, d, d)) | (~q2(d, b, d))),
% 1.10/0.97 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.10/0.97 tff(192,plain,
% 1.10/0.97 ($false),
% 1.10/0.97 inference(unit_resolution,[status(thm)],[191, 185, 151, 141, 138, 98])).
% 1.10/0.97 % SZS output end Proof
%------------------------------------------------------------------------------